The present invention relates generally to magnetic resonance (MR) imaging or spectroscopy systems. More particularly, the present invention relates to a scheme for designing a radio frequency (RF) coil assembly for transmitting and/or receiving signals in MR imaging or spectroscopy systems.
In recent years, MR imaging and spectroscopy have developed into a joint modality capable of studying relatively large sized objects of interest, such as, human anatomy. MR images depicting parameters associated with nuclear spins (for example, protons associated with water in tissue) can provide information about the amount, type, and state of various tissues in the imaging region. MR spectroscopy permits the study of chemical processes, for example, in live organisms. The use of MR to produce images and spectroscopic studies of relatively large sized objects of interest is made possible, in part, by specifically designed system components, such as, RF coil assemblies.
The MR phenomenon occurs in atomic nuclei having an odd number of protons or neutrons. Due to the spins of protons and neutrons, each nucleus associated with such a proton exhibits a magnetic moment. When an object of interest composed of such nuclei is subjected to a uniform or static magnetic field (polarizing field Bo, along the z direction in a Cartesian coordinate system denoted as x, y, and z), the individual magnetic moments of the spins in the nuclei tend to align with this polarizing field; but may also be made to precess about it at their characteristic Larmor frequency. The Larmor frequency, also referred to as the angular precession frequency T, is given by the Larmor equation T=xcex3B, where xcex3 is a gyromagnetic ratio characteristic of each active MR isotope and B is the magnetic field acting upon the nuclear spins (polarizing field Bo). Thus, the Larmor frequency is dependent on the strength of the applied static magnetic field and on the characteristics of the nuclei comprising the object of interest.
The orientation of the magnetic moments produce a net magnetization M in the direction along polarizing field Bo. Magnetization M, however, may be perturbed by the application of magnetic fields oscillating at or near the Larmor frequency. Such magnetic fields (referred to as an excitation field B1) are applied in a direction orthogonal to the direction of polarizing field Bo by means of radio frequency (RF) pulses through a coil connected to an RF transmitting apparatus. Under the influence of this RF excitation, magnetization M rotates or xe2x80x9cflipsxe2x80x9d at a certain flipping angle in the direction of excitation field B1. In MR studies, it is typically desirable to apply RF pulses of sufficient magnitude and duration to rotate or xe2x80x9cflipxe2x80x9d magnetization M into a plane perpendicular to the direction of polarizing field Bo (i.e., into the x-y plane, also referred to as a transverse plane) to produce a net transverse magnetic moment Mt. When RF excitation ceases, the nuclear moments that are rotated into the transverse plane nutate back toward the direction of polarizing field Bo. The vector sum of the moments of individual spins forms a precessing bulk magnetization that can be sensed by an RF coil. The signals emitted by the excited spins and received by the RF coil, also referred to as MR signals, are representative of the magnetic field and the particular chemical environment in which the nuclei are situated. MR signals are then suitably processed to produce an MR image or spectrum.
When MR signals are utilized to produce MR images, magnetic field gradients (Gx, Gy, and Gz) are also utilized to encode spatial information into these MR signals. Typically, the object to be imaged is scanned by a sequence of measurement cycles in which these gradient waveforms vary according to the particular localization method being used. The resulting set of received MR signals are digitized and processed to reconstruct the MR image using one of well-known reconstruction techniques.
RF coils used in whole-body MR studies can be a type of RF resonators known as transverse electromagnetic (TEM) resonators. Such an TEM resonator can be configured to be an RF receiver, transmitter, or transceiver. Presently, an TEM resonator is typically an open-ended structure and is configured to accommodate therein a part or all of a patient to be studied. The TEM resonator is cylindrical in shape, although, it need not be circular in cross-section. An TEM resonator includes a plurality of identical linear antenna elements, a pair of conductive annular rings, a cylindrical conductive shield, and capacitance.
The plurality of antenna elements are disposed in cylindrical array inside the shield, the linear axes of the antenna elements parallel with the cylindrical axis of the shield. One end of all of the antenna elements are held in place by one of the annular rings and the other end of all the antenna elements are held in place by the other one of the annular rings. The annular rings (also referred to as the annuli) are positioned inside and close to the ends of the shield. A certain amount of capacitance, either lumped or distributed, is also provided by discrete capacitors placed between the ends of each of the antenna elements and the annular rings, or by the device itself, respectively. An electrical circuit is thereby formed by each of the antenna elements, the pair of annular rings, the shield, and the capacitance, in which the shield and annular rings serve as a single ground plane and the shield contains the electromagnetic field within the cavity formed by the device.
Physical dimensions associated with the TEM resonator and of the various components comprising the TEM resonator comprise the geometric parameters of the TEM resonator. To a certain extent, the geometric parameters of TEM resonators are constrained by use and system requirements. For example, the diameter of the TEM resonator, and accordingly, the diameter of the shield and annular rings, is required to be of a certain minimum dimension to accommodate an object of interest, such as, a patient. The degree of mechanical symmetry and robustness desired may also dictate some geometric parameters. Material properties or cost considerations may further dictate geometric parameters.
In addition to geometric parameter constraints, TEM resonators also have electrical requirements, such as, having to operate at a principal or useful resonant mode frequency in order to receive the MR signals emitted from the object of interest. This principal or useful resonant mode frequency (also referred to as the operating frequency) is a resonant frequency associated with the overall device and should be the same as the Larmor frequency. In practice, however, designing an TEM resonator to operate at the desired principal resonant frequency is not a simple task. The design process involves balancing and determining numerous parameters, such as, geometry, material characteristics, electrical properties, number of subcomponents, etc., that satisfy the constraints discussed above.
Accordingly, designing an TEM resonator presently involves a long and laborious process of trial and error that typically takes several weeks to complete. The design process includes deciding on the physical dimensions or geometric parameters and fully constructing a working prototype of the desired TEM resonator based thereon. Then electrical parameters associated with the working prototype are measured, especially the resonant frequencies of the device. These measured parameters are used to construct a next iteration of the working prototype. This iterative process continues till the design parameters necessary to achieve the desired principal resonant frequency have been empirically determined.
Such iterative determinations are necessary due to the complex relationship between the design parameters and because not all of the design parameters can be determined directly through numerical or analytical calculations. For example, the principal resonant mode frequency is a function of the individual resonant frequency and the interaction (i.e., mutual coupling) between the antenna elements. The individual resonant mode frequency, in turn, is a function of the capacitance associated therewith (e.g., the lumped capacitance employed at both ends of a given antenna element). Accordingly, if magnetic coefficients of coupling (which express the degree of coupling or interaction between the antenna elements) can be calculated or approximated for an TEM resonator of a given geometry and which is to be operated at a certain principal resonant frequency, the design process can be completed merely by making a relatively few capacitance adjustments, as needed, to attain the desired resonant frequency.
Thus, there is a need for an TEM resonator designing scheme that reduces the design time, and which provides, numerically or analytically, the magnetic coefficients of coupling values. There is a further need for an TEM resonator designing scheme that can determine the capacitance based on the magnetic coefficients of coupling and the desired principal resonant frequency.
One exemplary embodiment relates to a method for designing a radio frequency (RF) coil assembly. The RF coil assembly has a plurality of antenna elements captured between two annular members and which are encircled by a shield. The RF coil assembly has rotational symmetry. The method includes determining a self inductance associated with any one of the antenna elements by solving analytically or numerically two-dimensional boundary value problems. The method further includes determining at least one mutual inductance associated with an one and an another of the antenna elements by solving analytically or numerically two-dimensional boundary value problems. The method still further includes determining at least one magnetic coefficient of coupling associated with the one and the another of the antenna elements, the at least one magnetic coefficient of coupling expressed as a ratio of the self inductance and the at least one mutual inductance.
Another exemplary embodiment relates to a system for designing a radio frequency (RF) coil assembly. The assembly includes a plurality of antenna elements captured between two annular members and which are encircled by a shield. The RF coil assembly has rotational symmetry. The system includes a computer configured to determine a self inductance associated with any of the antenna elements by solving two-dimensional boundary value problems, and determining a mutual inductance between a first and a second of the antenna elements by solving two-dimensional boundary value problems. The system further includes determining a magnetic coefficient of coupling associated with the first and the second of the antenna elements. The magnetic coefficient of coupling is expressed as a ratio of the self inductance and the mutual inductance.
Another exemplary embodiment relates to a system for designing a radio frequency (RF) coil assembly having a plurality of antenna elements between two annular members and which are encircled by a shield. The RF coil assembly has rotational symmetry. The system includes means for determining a self inductance associated with any one of the antenna elements by solving analytically or numerically two-dimensional boundary value problems, and means for determining at least one mutual inductance associated with an one and an another of the antenna elements by solving analytically or numerically two-dimensional boundary value problems. The system further includes means for determining at least one magnetic coefficient of coupling associated with the one and the another of the antenna elements. The at least one magnetic coefficient of coupling is expressed as a ratio of the self inductance and the at least one mutual inductance.
Still another exemplary embodiment relates to a radio frequency (RF) coil assembly having a plurality of antenna elements captured between two annular members and encircled by a shield. The RF coil assembly is designed by the steps including specifying geometry parameters associated with the RF coil assembly to be designed, and determining a self inductance associated with any one of the antenna elements by solving two-dimensional boundary value problems. The designing steps further include determining mutual inductances between the antenna elements by solving two-dimensional boundary value problems, and determining magnetic coefficients of coupling using the self inductance and the mutual inductances. The designing step still further include determining an individual antenna element frequency corresponding to a principal resonant mode frequency that is equal to a desired Larmor frequency, and determining a capacitance value of a capacitance applied to the ends of the antenna elements.
Yet still another exemplary embodiment relates to a radio frequency (RF) coil assembly, having a central longitudinal axis, for magnetic resonance (MR) imaging or spectroscopy. The assembly includes n antenna elements concentrically positioned within a shield. A longitudinal axis of each of the n antenna elements and of the shield are in parallel with the central longitudinal axis. The assembly further includes a pair of annular members coupled to both ends of the n antenna elements. Each of the annular members includes a bolt circle. The assembly still further includes a capacitance provided at each end of the n antenna elements. The assembly operates at a principal resonant mode frequency that is approximately equal to a desired Larmor frequency. A capacitance value of the capacitance is determined by calculating magnetic coefficients of coupling and an individual antenna element frequency using two-dimensional boundary value problems and a circuit theory of a bird-cage resonator. At least one of the magnetic coefficients of coupling and the individual antenna element frequency functions of physical dimensions of the antenna elements, the shield, and the annular members.